Solve for p

3+|1+p|=12

Subtract 3 from both sides

simplify 12 - 3 to 9

break down the problem into these two equations

1 + p = 9 and - (1 + p) = 9

solve the first equation 1 + p = 9 and that would be 8 since 1 + 8 = 9 is true.

solve the second equation - (1 + p) = 9 and just simplify brackets and add 1 to both sides then add 9 + 1 and lastly multiply both sides by - 1 and p = - 10.

Gather both solutions

Answers: p = - 10, 8